PHYSICAL REVIEW B VOLUME 47, NUMBER 22 1 JUNE 1993-II Spectral diffusion of molecular electronic transitions in amorphous solids: Weak and strong two-level-system phonon coupling R. Jankowiak and G. J. Small Department of Chemistry and Ames Laboratory, Iowa State University, Ames, Iowa 50011 (Received 19 November 1992; revised manuscript received 16 February 1993) The two-level-system (TLS) model of glasses is used with nonphenomenological TLS distribution func- tions [R. Jankowiak et ai. , J. Phys. Chem. 90, 3896 (1986)] to account for the time-dependent spectral- diffusion data for cresyl violet and zinc porphin in ethanol glasses at low temperatures [K. A. Littau and M. D. Fayer, Chem. Phys. Lett. 176, 551 (1991); H. C. Meijers and D. A. Wiersma, Phys. Rev. Lett. 68, 381 (1992)]. The two distributions of faster and slower TLS relaxation rates required to fit the data are characterized for both weak and strong TLS-phonon coupling. Comparison of the values obtained for the TLS parameters with those determined earlier for specific heat, thermal conductivity, pure dephas- ing, and spontaneous filling of nonphotochemical holes establishes that the faster and slower distribu- tions are associated with intrinsic and extrinsic TLS. The pronounced effects of strong coupling on the TLS relaxation-rate distributions are discussed. I. INTRODUCTION That the widths of the zero-phonon lines (ZPL) of im- purity molecules and R + ions imbedded in amorphous hosts are anomalous in their magnitude and temperature dependence for T~ 10 K has been known since the late 1970's (for recent reviews see Refs. 1 — 7). Initially, per- sistent nonphotochemical hole burning ' (NPHB) ' was used to probe the T dependence of the ZPL profile in or- ganic systems. Earlier, a mechanism for NPHB had been proposed that is based on phonon-assisted tunneling of a static distribution of two-level systems (TLS) inti- mately associated with the impurity. These TLS's are now referred to as extrinsic, TLS„, . Shortly thereafter, it was proposed that the anomalously large optical linewidths of impurity molecules, with their near linear dependence on temperature, were a manifestation of the interaction between the impurity and a different, faster relaxing type of TLS, now recognized to be intrinsic to the glass host, TLS;„, . The same conclusion was indepen- dently reached for R + ions in inorganic glasses. ' Theories of pure dephasing from impurity TLS;„, cou- pling, in which the off-diagonal ' ' or diago- nal' "" ' modulation terms of the impurity TLS in- teraction Hamiltonian were considered, rapidly emerged. Until 1986, ' ' theories were guided by the phenomeno- logical TLS distribution function of Anderson, Halperin, and Varma and Phillips; namely, P(b, , A, )=const for A, ~A, „and 6;„~h~h „and zero otherwise. Here A, and 6 are the TLS tunnel and asymmetry param- eters. The tunnel state splitting is E =(b, + W )' where the tunneling frequency &=coo exp( — k) and too 1s the average harmonic frequency of the two wells of the TLS. The above distribution function leads to a density of states p(E) — const. Utilization of phenomenological distribution functions in dephasing theories for averaging over the TLS interacting with the impurity necessitates assumptions' '' beyond that of an absence of correla- tion between 6 and A, . The dephasing theories have also taken the TLS-phonon interaction to be weak. Thermal-cycling-hole-burning experiments had proven early on that ' broadening of the zero-phonon hole (ZPH) occurs by spectral diffusion induced by slow thermally assisted, irreversible glass relaxation processes with the impurity in its ground state. However, it has only been recently ' that the question of the contri- bution of spectral diffusion to persistent nonphotochemi- cal, photochemical, and transient population bottleneck ZPH's produced under normal protocol has been actively pursued. By normal it is meant that the burn and read temperatures ( Ttt, Ttt ) are the same. In the thermal-cycle experiment the hole is burned and read at T~, the sample temperature raised to T) T~, then lowered to T~ and the hole read again. The resulting partial thermal annealing of the hole is accompanied by broadening. ' ' Given the result from thermal cycling, that the longitudinal relaxa- tion time (r, ) of the typical probe molecule is short, a few ns, and the time dependence of the specific heat, it would be reasonable to expect a contribution to the ZPH width from spectral diffusion when the waiting and read- ing times (t~, tR ) are long. In a series of beautiful two- pulse photon echo and NPHB experiments with resorufin and cresyl violet in alcohol (ethanol, glycerol) glasses Fayer and co-workers ' ' ' ' determined that the homogeneous width of the ZPL determined by photon echo is substantially narrower ( — X6) than that deter- mined by NPHB for T ~ 8 K. They ascribed the difference to spectral diffusion. Although later NPHB experiments on the same systems by Volker and co- workers ' ' led to some controversy concerning the magnitude and temperature dependence of the spectral diffusion reported by Fayer and co-workers, very recent two-pulse photon echo and fast ( 2 10 ps) hole-burning experiments by Littau and Fayer and Littau et al. on cresyl violet in ethanol glass, stimulated photon echo experiments by Meijers and Wiersma on zinc porphin in 0163-1829/93/47(22)/14805(8)/$06. 00 47 14 805 1993 The American Physical Society